Abstract
Via Phi-Sobolev inequalities, we give some sharp integrability conditions on $F$ for the large deviation principle of the empirical mean $\frac{1}{T}{\int_{0}^{T}{F(X_{s})}ds}$ for large time $T$, where $F$ is unbounded with values in some separable Banach space. Several examples are provided.
Citation
Liming Wu. Nian Yao. "Large deviation principles for Markov processes via Phi-Sobolev inequalities." Electron. Commun. Probab. 13 10 - 23, 2008. https://doi.org/10.1214/ECP.v13-1342
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